A major index for matchings and set partitions

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We introduce a statistic $\pmaj$ on partitions of $[n]=\{1,2,..., n\}$, and show that it is equidistributed with the number of 2-crossings over partitions of $[n]$ with given sets of minimal block elements and maximal block elements. This generalizes the classical result of equidistribution for the permutation statistics inversion number and major index.
17 pages, 9 figures

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Combinatorics, 05A18, 05A15

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http://salesiana.dossiersoluciones.com/handle/123456789/121046

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701096
 http://arxiv.org/abs/math/0701096

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arXiv